Existence results for second order linear differential equations in Banach spaces

Abstract

In this paper we are concerned with the existence of solutions for certain classes of second order differential equations. First we deal with an infinite system of second order linear differential equations, which is reduced to an ordinary differential equation posed in the space of convergent sequences. Next we investigate the problem of existence for a second order differential equation posed on an arbitrary Banach space. The used approach is based on the measures of noncompactness concept, the use of Darbo's fixed point theorem and Kamke comparison functions.